Homework Helpers: Physics

6 Electric Current and Circuits

We said that the bulb in our flashlight glows because the filament in the bulb is a resistor, which converts the electrical energy of the charged particles into heat and light. However, you may have noticed that the bulbs that you buy are sorted by watts (W), a unit of power—not ohms, a unit of resistance. We encountered the unit called watts when we studied power in Chapter 3. In this lesson we will study electric power, which is the rate at which electrical energy is converted into other forms of energy, such as heat, light, and/or kinetic energy.

Example 1

A bulb operates at 40.0 mW when connected to a 9.0 V battery. Find both the current through and the resistance offered by the bulb.

Convert: The small “m” before the symbol for watts (as in 40.0 mW) stands for “milli.”

Notice that the way we write the answer, 4.00 × 10^–2 W, retains the same number of significant digits as our original value of 40.0 mW.

Let”s not use this value for I to find R. Remember: I always recommend using only the original givens to find unknowns in multiple part questions (whenever possible) to avoid carrying over errors to other calculations.

The Cost of Electric Power

Many textbooks stress the fact that what we call “power companies” really charge us for is energy, not power. The “power” company doesn”t care about the rate that we use the electrical energy, just the total amount that we use. If we use 2,500 joules in 10 minutes or in 10 days, it still costs us the same amount. If you ever look at the bill that comes from you “power” company, you will see that you are being charged a certain amount of money per kilowatt-hour (kW-h). Kilowatts are units of power, and hours are units of time. If you multiply power by time, you get work, which can be measured in joules, or kilowatt-hours.

Lightbulbs and many of your appliances list their power ratings somewhere on them. Other appliances will list the current they draw and the operating voltage. Check on the back of your TV or the bottom of your toaster oven. By checking the power rating of various appliances and the amount of money your family is being charged per kilowatt-hour, you can calculate approximately how much it is costing you (or your parents) to run these appliances.

cost = energy × rate

C = ER

Example 2

My toaster oven has a power rating of 1,500 W. If I am charged $0.12 per kilowatt-hour, and I run my toaster oven for 8.0 minutes every day, approximately how much is this costing me per month?

Convert: We must change watts to kilowatts.

Let”s also convert 8.0 minutes per day to hours/month.

Now, we can calculate the number of kW-h I am using to run the toaster each month.

1.5 kW × 4.0 h = 6.0 kW-h

So, I am only spending about 72 cents to run my toaster each month. It is always surprising to see how little certain appliances cost to use. It may make you wonder why the electric bill can get so high at times, or why your parents always told you to shut off the lights when you left the room. Remember: There are probably quite a few appliances and bulbs in your home, and all of those little charges add up. More importantly, some appliances with higher power ratings probably account for a relatively large portion of your monthly bill. Refrigerators, air conditioners, dryers, and hot-water heaters draw much more power than your toaster oven, so they cost your family more per hour that they are in operation.

Lesson 6–3 Review

1. What is the current through a 40.0 W bulb with a voltage of 120 V across it?

2. A hair dryer draws 8.2 A of current from a 120-volt outlet. What is the power rating for the toaster?

3. Calculate the current through a 3.0Ω resistor that operates at 60.0 W.

4. Calculate the power rating of a bulb that offers 160Ω of resistance with a current of 0.50 A through it.

5. My laptop has a power rating of 80.0 W. if I pay $0.17/kW-h for my electricity, how much will it cost me to use my laptop for 8.0 hours?